3 citations · 7 across the 9 of their papers we have counts for
10 papers
Connecting orbits in quasiaffine spherical varieties via -root subgroups
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group with a Borel subgroup and a quasiaffine spherical -variety , we prove that every -orbit contained in the regular lo…
Root subgroups on horospherical varieties
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group and a spherical -variety , a -root subgroup on is a one-parameter additive group of automorphisms of normalized by…
On the existence of -root subgroups on affine spherical varieties
Roman Avdeev, Vladimir Zhgoon
Let be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group . In this paper we provide sufficient conditions, f…
Complexity of actions over perfect fields
Friedrich Knop, Vladimir S. Zhgoon
Let be a connected reductive group over a perfect field acting on an algebraic variety and let be a minimal parabolic subgroup of . For -spherical -varieti…
Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties
Dmitry A. Timashev, Vladimir S. Zhgoon
We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of…
On the embeddings of universal torsors over del Pezzo surfaces in the cones over flag varieties
Vladimir S. Zhgoon
Following Skorobogatov and Serganova we construct the embeddings of universal torsors over del Pezzo surfaces in the cones over flag varieties, considered as the closed orbits in t…
On the Local structure theorem and equivariant geometry of cotangent bundles
Vladimir S. Zhgoon
Let be a connected reductive group acting on an irreducible normal algebraic variety . We give a slightly improved version of local structure theorems obtained by F.Knop and…
Angle measures of some cones associated with finite reflection groups
Pavel V. Bibikov, Vladimir S. Zhgoon
We give a generalization of "Curious Identity" of De Concini and Procesi. Our proof is based on the recent result of Waldspurger about the decomposition of the cone dual to the fun…
On tilings defined by discrete reflection groups
Pavel V. Bibikov, Vladimir S. Zhgoon
The recent articles of Waldspurger and Meinrenken contained the results of tilings formed by the sets of type , , where is a linear or affine Weyl group,…
Variation of Mumford's quotients for the maximal torus action on a flag variety
Vladimir S. Zhgoon
We study a variation of Mumford's quotient for the action of a maximal torus on a flag variety depending on projective embedding , where…